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Data Analysis Tips
MCMC and Bayesian in application Basics * Metropolis-Hastings algorithm Crash Course * [http://www.phas.ubc.ca/~gregory/gregory.html Materials from Phil Gregory's Website] * [http://astrostatistics.psu.edu/ Material from Center for Astrostatistics website] * [http://conference.scipy.org/scipy2011/tutorials.php#christopher An Introduction to Bayesian Statistical Modeling using PyMC - Christopher J. Fonnesbeck and Abie Flaxman on SciPy2011] ** There are plenty other useful courses about SciPy and Python. ** The Video content is GFW unfriendly!! * Your Gateway to the Bayesian Realm on Astrobites ** Very good place to start !! * Code you can use: the MCMC Hammer on Astrobites ** Introduction to emcee * PyMC for Bayesian models ** Nice example for PyMC GFW!! * More on MCMC in Python on science,stories,etc blog ** Astrophysical related blog, provide a slightly more complex example. GFW!! * MCMC and fitting models to data from Scientific Clearing House blog GFW!! ** Two relevant posts: Bayesian parameter estimation and Bayesian model comparison * Gibbs sampler in various languages (revisited) from Darren Wilkinson's research blog ** Including Python, PyPy and C. ** There are other useful posts on this blog GFW!! * Astrostatistics Seminar Series @UFL ** Including Bayesian Data Analysis for the Physical Sciences by Phill Gregory; and A Bayesian toolbox for testing models in astronomy by Martin Hendry * 实用统计软件 ** 部分内容可能有帮助 Reference * Bayes in the sky: Bayesian inference and model selection in cosmology * Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications Useful Tools * [https://github.com/pymc-devs/pymc PyMC] ** PyMC is a python module that implements Bayesian statistical models and fitting algorithms, including Markov chain Monte Carlo. Its flexibility and extensibility make it applicable to a large suite of problems. Along with core sampling functionality, PyMC includes methods for summarizing output, plotting, goodness-of-fit and convergence diagnostics. ** Using Metropolis-Hartings algorithm ** The document can be found here * [http://code.google.com/p/bayesian-inference/ bayesian-inference - Python package for object-oriented bayesian inference] ** This package is a collection of useful classes for basic Bayesian inference. Currently, its main goal is to be a tool for learning and exploration of Bayesian probabilistic calculations. ** The documentations can be found here * [http://ccpforge.cse.rl.ac.uk/gf/project/multinest/ MultiNest-Efficient and Robust Bayesian Inference] ** MultiNest is a Bayesian inference tool which calculates the evidence and explores the parameter space which may contain multiple posterior modes and pronounced (curving) degeneracies in moderately high dimensions. ** A python wrapper: [http://code.google.com/p/lisasolve/wiki/pymultinest pymultinest] * [http://www.hs.uni-hamburg.de/DE/Ins/Per/Czesla/PyA/PyA/funcFitDoc/index.html funcFit-A convenient fitting interface in PyAstronomy] *** The funcFit package provides a convenient interface to the fitting algorithms provided by the popular SciPy and pymc packages. It implements a very flexible and simple parameter handling mechanism making fitting in Python a much more enjoyable experience. * [https://github.com/bayespy/bayespy BayesPy] ** BayesPy provides tools for Bayesian inference with Python. The user constructs a model as a Bayesian network, observes data and runs posterior inference. The goal is to provide a tool which is efficient, flexible and extendable enough for expert use but also accessible for more casual users. * [http://flux.aos.wisc.edu/data/code/mcmc/ MCMC-IDL by Ankur Desai] * IDL Codes by Chris Beaumont * [http://idlastro.gsfc.nasa.gov/ftp/pro/math/linmix_err.pro LINMIX_ERR], and [http://idlastro.gsfc.nasa.gov/ftp/pro/math/mlinmix_err.pro MLINMIX_ERR] by Brandon Kelly Mixture Gaussian and the Modelling of Histograms * 关于Mixture Model的Wikipedia词条 * 漫谈 Clustering (3): Gaussian Mixture Model: Blog from Free Mind * Lecture about GMM by Douglas Reynolds @ MIT Potential Tools * [http://www.ast.cam.ac.uk/~vasily/solber/ Solber-Solution Breeder] ** Solber is a simple IDL optimization routine loosely based on genetic algorithms ** The code can be found here; and example about Mixture Gaussian model can be found here ** The webpage of the author also includes very interesting information. ** Papers about the algorithm behind Solber can be found here * [http://code.google.com/p/extreme-deconvolution/ XD-Extreme Deconvolution] ** Density estimation using Gaussian mixtures in the presence of noisy, heterogeneous and incomplete data ** The associated arXiv paper can be found here ** Examples about its application is here ** Referred papers using XD is here * [http://astroml.github.com/book_figures/chapter6/fig_stellar_XD.html Extreme Deconvolution using the AstroML Python Library] ** Another similar one * [http://www.pymix.org/pymix/index.php?n=PyMix.Home PyMix] ** The Python Mixture Package (PyMix) is a freely available Python library implementing algorithms and data structures for a wide variety of data mining applications with basic and extended mixture models ** The tutorial can be found here * [http://cran.r-project.org/web/packages/mixtools/index.html mixtools in R package] ** A collection of R functions for analyzing finite mixture models. ** Documents for this package can be found Here ** A blog article about how to use it (GFW unfriendly) * [http://pypr.sourceforge.net/ PyPR-Python Pattern Recognition] * [http://www.ar.media.kyoto-u.ac.jp/members/david/softwares/em/index.html em-a python package for Gaussian mixture models] ** Since July 2007, the toolbox is included in the learn scikits (scikits). * [http://code.google.com/p/ecgmm/ ECGMM-Error Corrected Gaussian Mixture Model] ** Traditional Gaussian Mixture Model does not handle the measurement errors of each data point. In many applications, the data point themselves are uncertain to certain level and then a error corrected (or weighted if you would like) Gaussian Mixture Model is desirable.